Beginning Algebra, 11th Edition

(b)

Cube each side.

Apply the exponents.

Standard form

Factor.

or Zero-factor property

or Solve.

CHECK

Let Let

✓ True ✓ True

Both proposed solutions check, so the solution set is 5 - 1, 27 6. NOW TRY

1 = 1 9 = 9

231  231 23729  23729

x=-1. x=27.

231 - 122  23261 - 12 + 27 2312722  23261272 + 27

23 x^2 = 2326 x+ 27 23 x^2 = 2326 x+ 27

x=- 1 x= 27

x+ 1 = 0 x - 27 = 0

1 x+ 121 x- 272 = 0

x^2 - 26 x- 27 = 0

x^2 = 26 x+ 27

A 23 x^2 B

3

=A 2326 x+ 27 B

3

23 x^2 = 2326 x+ 27

536 CHAPTER 8 Roots and Radicals

NOW TRY
EXERCISE 8
Solve each equation.

(a)

(b) 232 x^2 = 2310 x- 12

238 x- 3 = 234 x

NOW TRY ANSWERS

8. (a)E^34 F (b) 5 2, 3 6

Complete solution available
on the Video Resources on DVD

8.6 EXERCISES

Solve each equation. See Examples 1–4.

1. 
   
   
   
   2. 
      
      
      
      3. 
         
         
         
         4. 
            
         
         
         
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   6. 
      
      
      
      7. 
         
         
         
         8. 
            
         
         
         
         
      
      
      
      
   
   
   
   


3. 
   
   
   
   10. 
       
       
       
       11. 
           
           
           
           12. 
               
           
           
           
           
       
       
       
       
   
   
   
   


4. 
   
   
   
   14. 
       
       
       
       15. 
           
       
       
       
       
   
   
   
   


5. 
   
   
   
   17. 
       
       
       
       18. 
           
       
       
       
       
   
   
   
   


6. 
   
   
   
   20. 
       
       
       
       21. 
           
       
       
       
       
   
   
   
   


7. 
   
   
   
   23. 
       
       
       
       24. 
           
       
       
       
       
   
   
   
   


8. 
   
   
   
   26. 
       
       
       
       27. 
           
       
       
       
       
   
   
   
   


9. 23 m+ 3 = 25 m- 1 29. 23 x- 8 =- 2 30. 26 t+ 4 =- 3

22 x+ 2 = 23 x- 5 2 x+ 2 = 22 x- 5 25 x- 5 = 24 x+ 1

x= 2 x^2 - 2 x- 6 7 x= 249 x^2 + 2 x- 10 6 x= 236 x^2 + 5 x- 5

23 x- 5 = 22 x+ 1 25 x+ 2 = 23 x+ 8 k= 2 k^2 - 5 k- 15

217 t- 4 = 42 t 52 x= 210 x+ 15 42 x= 220 x- 16

2 w- 4 = 7 2 t + 3 = 10 210 x- 8 = 32 x

22 t+ 3 = 0 25 x- 4 = 0 2 t =- 5 2 p=- 8

2 r- 4 = 9 2 x- 12 = 3 24 - t= 7 29 - s= 5

2 x= 7 2 x= 10 2 x+ 2 = 3 2 x+ 7 = 5

31.Concept Check Consider the following

“solution.”WHAT WENT WRONG?

Square each side.

Distributive property

Subtract 1.

Multiply by

Solution set: 5 - 156

x=- 15 - 1.

• x= 15


• x+ 1 = 16


• 1 x- 12 = 16


• 2 x- 1 =- 4

32.Concept Check The first step in solving

the equation

is to square each side of the equation.

Errors often occur in solving equations

such as this one when the right side of

the equation is squared incorrectly. What

is the square of the right side?

22 x+ 1 =x- 7

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